Presentation is loading. Please wait.

Presentation is loading. Please wait.

Isomorphism: A First Example MAT 320 Spring 2008 Dr. Hamblin.

Published byJessie Greer Modified over 9 years ago

Similar presentations

Presentation on theme: "Isomorphism: A First Example MAT 320 Spring 2008 Dr. Hamblin."— Presentation transcript:

1 Isomorphism: A First Example MAT 320 Spring 2008 Dr. Hamblin

2 Are Z 5 and S = {0,2,4,6,8}  Z 10 the same? +01234·01234 001234000000 112340101234 223401202413 334012303142 440123404321 +02468·02468 002468000000 224680204826 446802408642 668024602468 880246806284

3 Using colors to decide… +01234·01234 001234000000 112340101234 223401202413 334012303142 440123404321 +02468·02468 002468000000 224680204826 446802408642 668024602468 880246806284

4 It seems like the answer is no… Color-coding the elements of each ring shows that the multiplication tables don’t match up However, notice something in the multiplication table for S: This shows that 1 S = 6 Since 1 in Z5 was colored green, this means our coloring was wrong!

5 Start with empty tables and fill in based on color… +01234·01234 001234000000 112340101234 223401202413 334012303142 440123404321 +06·06 006000 66606 66 66 66

6 Since 6+6=2 in S, 2 is yellow… +01234·01234 001234000000 112340101234 223401202413 334012303142 440123404321 +062·062 00620000 6626062 2262026 662 626

7 It follows that 8 is blue and 4 is purple +01234·01234 001234000000 112340101234 223401202413 334012303142 440123404321 +06284·06284 006284000000 662840606284 228406202468 884062808642 440628404826

8 With this new coloring… …we see that the two rings have exactly the same structure When two rings have exactly the same addition and multiplication tables (under some correspondence between their elements), we say the rings are isomorphic iso = same, morphic = structure Finding the correspondence is the hard part!

Download ppt "Isomorphism: A First Example MAT 320 Spring 2008 Dr. Hamblin."

Similar presentations

We Can Read About Mixing Colors

We Can Read About Mixing Colors
How many squares are there on a chess board?

How many squares are there on a chess board?
COLORING WITH NUMBERS. NumbersNumbers NumbersNumbers 1-61-6 1-61-6.

COLORING WITH NUMBERS. NumbersNumbers NumbersNumbers
© red ©

© red ©
1 st Grade Mathematics Students will have a basic understanding of adding numbers. Students will have basic word problem skills. Students will know basic.

1 st Grade Mathematics Students will have a basic understanding of adding numbers. Students will have basic word problem skills. Students will know basic.
Patterns IN THE PERIODIC TABLE PROJECT

Patterns IN THE PERIODIC TABLE PROJECT
Mrs. Smith’s 7th Grade Reading Blue Class Mrs. Smith’s 7th Grade Reading Blue Class Mrs. Smith’s 7th Grade Reading Blue Class.

Mrs. Smith’s 7th Grade Reading Blue Class Mrs. Smith’s 7th Grade Reading Blue Class Mrs. Smith’s 7th Grade Reading Blue Class.
Section 1.1: Integer Operations and the Division Algorithm

Section 1.1: Integer Operations and the Division Algorithm
Isomorphisms This is when seemingly different things seem to be governed by the same rules. Example You know that Arg(z 1  z 2 ) = Arg(z 1 ) + Arg(z 2.

Isomorphisms This is when seemingly different things seem to be governed by the same rules. Example You know that Arg(z 1  z 2 ) = Arg(z 1 ) + Arg(z 2.
The Color Wheel Claire Heider The Primary Colors.

The Color Wheel Claire Heider The Primary Colors.
Kids S1 Vocabulary U1 Colors. Listen and say the color:

Kids S1 Vocabulary U1 Colors. Listen and say the color:
COUNTING Directions: Write your word on the I pad and on the paper. Count the amount of letters in your word and then find the color that matches that.

COUNTING Directions: Write your word on the I pad and on the paper. Count the amount of letters in your word and then find the color that matches that.
If you say 8 color the ones in your picture purple. If you say 9 color the ones in your picture blue.

If you say 8 color the ones in your picture purple. If you say 9 color the ones in your picture blue.
By: Elizabeth Hayden Mrs. Valle Art Class.  I learned a great song that showed and taught me the primary and secondary colors.  I learned how the primary.

By: Elizabeth Hayden Mrs. Valle Art Class.  I learned a great song that showed and taught me the primary and secondary colors.  I learned how the primary.
Multiplication Facts 3 5 6 4 7 8 2 9 1. Table of Contents 0’s 1’s 2’s 3’s 4’s 5’s 6’s 7’s 8’s 9’s 10’s.

Multiplication Facts Table of Contents 0’s 1’s 2’s 3’s 4’s 5’s 6’s 7’s 8’s 9’s 10’s.
Fractional Parts of a Whole By:. What part of this object is colored red?

Fractional Parts of a Whole By:. What part of this object is colored red?
Key Events in North America Colored Maps Color Key France = red Spain = yellow US = blue Great Britain (England) = green Mexico = purple.

Key Events in North America Colored Maps Color Key France = red Spain = yellow US = blue Great Britain (England) = green Mexico = purple.
FRACTIONS & SHAPES BY:. How many of these are colored red? * out of *.

FRACTIONS & SHAPES BY:. How many of these are colored red? * out of *.
= 5 = 2 = 4 = 3 How could I make 13 from these shapes? How could I make 19 from these shapes? STARTER.

= 5 = 2 = 4 = 3 How could I make 13 from these shapes? How could I make 19 from these shapes? STARTER.
Directions: 1.Divide the class into two teams: X’s & O’s. Begin the game. 2.Once all characters have been introduced, you will come to a screen with all.

Directions: 1.Divide the class into two teams: X’s & O’s. Begin the game. 2.Once all characters have been introduced, you will come to a screen with all.

Similar presentations

Ads by Google